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1. A method comprising: identifying an input population of parent epsilon chromosome data structures, wherein each parent epsilon chromosome data structure provides genes each having a respective candidate epsilon value, each candidate epsilon value representing a respective step size or spacing associated with a respective problem objective of a plurality of problem objectives; selecting one or more pairs of parent epsilon chromosome data structures from the input population of parent epsilon chromosome data structures; combining genes of each selected pair of parent epsilon chromosome data structures according to at least one evolutionary operator to generate a plurality of child epsilon chromosome data structures, each child epsilon chromosome data structure providing one or more genes each having a respective candidate epsilon value representing a respective step size or spacing for the respective problem objective; and evaluating each of the plurality of child epsilon chromosome data structures according to one or more epsilon objective functions to generate respective epsilon objective function values for each child epsilon chromosome data structure, wherein each epsilon objective function is associated with a respective goal associated with at least one a priori criterion defined using at least a respective subset of the plurality of problem objectives, wherein each respective epsilon objective function value indicates an extent to which each respective goal can be achieved, wherein the prior steps are performed by one or more computers wherein the identifying, selecting, combining, and evaluating steps form an epsilon optimization process, and further comprising: selecting an epsilon chromosome data structure from one of the evaluated chromosome data structures, wherein candidate epsilon values from the selected epsilon chromosome data structure form an epsilon vector utilized in performing a problem optimization process, wherein the problem optimization process seeks to identify a set of epsilon non-dominated solutions for each respective subset of the plurality of problem objectives, wherein a size of the set of solutions for each subset is based at least in part on the epsilon vector.
A computer-implemented method optimizes solutions across multiple objectives by evolving "epsilon chromosomes." It starts with an initial set of these chromosomes, each containing candidate step sizes ("epsilon values") for each objective. Pairs of chromosomes are selected and combined using evolutionary techniques (like crossover or mutation) to create new "child" chromosomes. Each child's performance is then evaluated based on how well its epsilon values achieve predefined goals, which are based on subsets of the objectives. The best chromosome is selected, and its epsilon values are used to guide a problem optimization process to find a diverse set of near-optimal solutions for each objective subset. The size of each solution set is influenced by the chosen epsilon values.
2. The method of claim 1 , wherein the respective a priori criterion is associated with a number of desired solutions within a respective problem search space defined by the respective subset of the plurality of problem objectives.
Building upon the optimization method, the predefined goal for each objective subset relates to achieving a desired *number* of solutions within the search space defined by that subset. In other words, the method aims to find a specific quantity of diverse solutions for each objective or combination of objectives, with the epsilon values helping to control how densely the solutions are distributed. This allows targeting a particular level of solution granularity.
3. The method of claim 2 , wherein the respective problem search space defined by the respective subset of the plurality of problem objectives is a total search space defined by an entirety of the problem objectives.
Further extending the optimization method, the desired number of solutions applies to the *entire* search space defined by *all* of the problem objectives combined. Instead of optimizing for solution counts within objective subsets, this variation focuses on achieving a specific number of solutions across the complete problem landscape, considering all objectives simultaneously.
4. The method of claim 2 , wherein the evaluating comprises sorting an archive of possible problem solutions using the respective step size or spacing of the respective candidate epsilon value of the respective child epsilon chromosome structure and evaluating the extent to which each respective goal of the number of desired solutions within the respective problem search space can be achieved.
In the optimization method, the evaluation step sorts potential solutions (stored in an archive) based on the step sizes from the child chromosome's epsilon values. The method then assesses how well the resulting solution distribution meets the goal of achieving the desired number of solutions within the defined search space. Thus, the method uses the epsilon values to directly organize the solutions and evaluate their suitability in achieving the target quantity.
5. The method of claim 1 , wherein the identified set of solutions is stored in an archive.
The method maintains an archive to store the identified set of near-optimal solutions generated during the optimization process. This archive serves as a repository of discovered solutions, allowing for later analysis, selection, or further refinement.
6. The method of claim 1 , wherein the epsilon optimization process is triggered following a termination of a first run of the problem optimization process, wherein upon completion of the epsilon optimization process, the epsilon vector is utilized in performing a second run of the problem optimization process.
The epsilon optimization process is triggered after an initial run of the problem optimization process completes. Once the epsilon optimization is finished, the new epsilon vector is then used for a second optimization run. This allows for adaptive refinement of the optimization parameters based on the results of the initial attempt.
7. The method of claim 1 , wherein the epsilon vector is a second epsilon vector, wherein the first run of the optimization process utilizes a first epsilon vector, wherein respective epsilon values of the second epsilon vector vary within one or more predefined ranges from epsilon values of the first epsilon vector.
The first optimization run uses a first epsilon vector. The subsequent epsilon optimization produces a *second* epsilon vector, where the epsilon values in the second vector are varied within a specified range around the epsilon values of the *first* epsilon vector. This allows the system to explore a neighborhood of epsilon values, refining the step sizes based on previous performance.
8. The method of claim 1 , wherein epsilon values in the epsilon vector are utilized in performing the second run of the second optimization process.
The epsilon values from the selected epsilon vector are used to perform the second optimization process.
9. The method of claim 1 , wherein the respective a priori criterion is associated with a minimum spacing requirement of solutions within a respective problem search space defined by the respective subset of the plurality of problem objectives.
The a priori criterion is associated with a *minimum spacing* requirement between solutions within the respective problem search space defined by the respective subset of the plurality of problem objectives.
10. The method of claim 1 , wherein a number of subsets of the plurality of problem objectives being utilized for a problem optimization process is equal to a total number of the one or more epsilon objective functions.
The number of subsets of problem objectives used for optimization is equal to the total number of epsilon objective functions.
11. The method of claim 1 , wherein each problem objective is associated with a minimization or a maximization of a respective dimension.
Each problem objective is associated with either minimizing or maximizing a corresponding dimension.
12. The method of claim 1 , wherein the at least one evolutionary operator includes one or both of a cross-over operator or a mutation operator.
The evolutionary operator includes one or both of a crossover operator or a mutation operator.
13. The method of claim 1 , wherein at least a portion of the identified input population of parent epsilon chromosome data structures is randomly generated.
At least some of the initial "parent" epsilon chromosomes are created randomly. This introduces diversity into the starting population, allowing the evolutionary process to explore a wider range of potential epsilon values.
14. A system comprising: at least one memory that stores computer-executable instructions; and at least one processor configured to access the at least one memory, wherein the at least one processor is configured to execute the computer-executable instructions to: identify an input population of parent epsilon chromosome data structures, wherein each parent epsilon chromosome data structure provides genes each having a respective candidate epsilon value, each candidate epsilon value representing a respective step size or spacing associated with a respective problem objective of a plurality of problem objectives; select one or more pairs of parent epsilon chromosome data structures from the input population of parent epsilon chromosome data structures; combine genes of each selected pair of parent epsilon chromosome data structures according to at least one evolutionary operator to generate a plurality of child epsilon chromosome data structures, each child epsilon chromosome data structure providing one or more genes each having a respective candidate epsilon value representing a respective step size or spacing for the respective problem objective; and evaluate each of the plurality of child epsilon chromosome data structures according to one or more epsilon objective functions to generate respective epsilon objective function values for each child epsilon chromosome data structure, wherein each epsilon objective function is associated with a respective goal associated with at least one a priori criterion defined using at least a respective subset of the plurality of problem objectives, wherein each respective epsilon objective function value indicates an extent to which each respective goal can be achieved wherein the identifying, selecting, combining, and evaluating from an epsilon optimization process, and wherein the at least one processor is further configured to execute the computer-executable instructions to: select an epsilon chromosome data structure from one of the evaluated chromosome data structures, wherein candidate epsilon values from the selected epsilon chromosome data structure form an epsilon vector utilized in performing a problem optimization process, wherein the problem optimization process seeks to identify a set of epsilon non-dominated solutions for each respective subset of the plurality of problem objectives, wherein a size of the set of solutions for each subset is based at least in part on the epsilon vector.
A computer system is designed to optimize solutions across multiple objectives. It includes memory to store instructions and a processor to execute them. The processor identifies an initial set of "epsilon chromosomes," each with candidate step sizes ("epsilon values") for each objective. It selects and combines pairs of chromosomes to create "child" chromosomes using evolutionary operators. The processor evaluates each child based on how well its epsilon values achieve predefined goals, which are based on subsets of the objectives. The best chromosome's epsilon values are then used to guide a problem optimization process to find a diverse set of near-optimal solutions for each objective subset. The size of each solution set is influenced by the chosen epsilon values.
15. The system of claim 14 , wherein the respective a priori criterion is associated with a number of desired solutions within a respective problem search space defined by the respective subset of the plurality of problem objectives.
Expanding on the system description, the predefined goal for each objective subset focuses on achieving a desired *number* of solutions within the search space defined by that subset. In other words, the system aims to find a specific quantity of diverse solutions for each objective or combination of objectives, using the epsilon values to control solution density. This enables fine-tuning the level of solution granularity.
16. The system of claim 15 , wherein the evaluation is performed by sorting an archive of possible problem solutions using the respective step size or spacing of the respective candidate epsilon value of the respective child epsilon chromosome structure and evaluating the extent to which each respective goal of the number of desired solutions within the respective problem search space can be achieved.
In the described system, the evaluation of child chromosomes involves sorting an archive of potential solutions based on the step sizes from the child chromosome's epsilon values. The system then assesses how well the resulting solution distribution meets the goal of achieving the desired number of solutions within the defined search space. Thus, epsilon values directly organize the solutions and support their suitability assessment.
17. The system of claim 14 , wherein the respective a priori criterion is associated with a minimum spacing requirement of solutions within a respective problem search space defined by the respective subset of the plurality of problem objectives.
Expanding on the system, the predefined goal focuses on a *minimum spacing* requirement between solutions within the problem search space. The step sizes within each chromosome define this spacing, which the evaluation assesses.
18. The system of claim 14 , wherein each problem objective is associated with a minimization or a maximization of a respective dimension.
Within the described system, each problem objective is associated with either minimizing or maximizing a corresponding dimension.
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October 14, 2014
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